Low emittance lattice design from first principles: reverse bending and longitudinal gradient bends

The well-known relaxed theoretical minimum emittance (TME) cell is commonly used in the design of multi-bend achromat (MBA) lattices for the new generation of diffraction limited storage rings. But significantly lower emittance at moderate focusing properties can be achieved by combining longitudinal gradient bends (LGB) and reverse bends (RB) in a periodic lattice unit cell. LGBs alone, however, are of rather limited gain. We investigate the emittance achievable for different unit cell classes as a function of the cell phase advance in a most general framework, i.e. with a minimum of assumptions on the particular cell optics. Each case is illustrated with a practical example of a realistic lattice cell, eventually leading to the LGB/RB unit cell of the baseline lattice for the upgrade of the Swiss Light Source

Design Of SRF Cavities With Cell Profiles Based On Bezier Splines

Elliptical cavities have been a standard in SRF linac technology for 30 years. In this work, we present a novel approach [1] using Bezier spline profile curves. By using different degrees of spline curves, the number of free parameters can be varied to suit a given problem endcell tuning, basecell figures of merit , thus leading to a high flexibility of the spline approach. As a realistic example, a cubic spline SRF multicell cavity geometry is calculated and the figures of merit are optimized for the operational mode. We also present an outline for HOM endcell optimization that can be realized using available 2D solver

Alternative Approaches for HOM Damped Cavities

In this paper, we present two different ideas that may be useful for design and simulation of superconducting radio frequency cavities. To obtain longitudinal and transverse voltages resp. shunt impedances in cavities without rotational symmetry, one or two integration paths are often used to get an approximate difference relation for the transverse voltage of higher order modes HOMs . The presented approach uses a multipole decomposition that is valid in vicinity of the central axis to compute voltage multipole decomposition directly for paths of arbitrary number and position. Elliptical cavities have been a standard in SRF linac technology for 30 years. We present another approach to base cell geometry based on Bezier splines that is much more flexible in terms of optimization, while reaching equal performance level

On the Nature of the Cosmological Constant Problem

General relativity postulates the Minkowski space-time to be the standard flat geometry against which we compare all curved space-times and the gravitational ground state where particles, quantum fields and their vacuum states are primarily conceived. On the other hand, experimental evidences show that there exists a non-zero cosmological constant, which implies in a deSitter space-time, not compatible with the assumed Minkowski structure. Such inconsistency is shown to be a consequence of the lack of a application independent curvature standard in Riemann's geometry, leading eventually to the cosmological constant problem in general relativity. We show how the curvature standard in Riemann's geometry can be fixed by Nash's theorem on locally embedded Riemannian geometries, which imply in the existence of extra dimensions. The resulting gravitational theory is more general than general relativity, similar to brane-world gravity, but where the propagation of the gravitational field along the extra dimensions is a mathematical necessity, rather than being a a postulate. After a brief introduction to Nash's theorem, we show that the vacuum energy density must remain confined to four-dimensional space-times, but the cosmological constant resulting from the contracted Bianchi identity is a gravitational contribution which propagates in the extra dimensions. Therefore, the comparison between the vacuum energy and the cosmological constant in general relativity ceases to be. Instead, the geometrical fix provided by Nash's theorem suggests that the vacuum energy density contributes to the perturbations of the gravitational field.Comment: LaTex, 5 pages no figutres. Correction on author lis

Supersymmetric version of a hydrodynamic system in Riemann invariants and its solutions

In this paper, a supersymmetric extension of a system of hydrodynamic type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and supersymmetric versions of this hydrodynamical model are analyzed through the use of group-theoretical methods applied to partial differential equations involving both bosonic and fermionic variables. More specifically, we compute the Lie superalgebras of both models and perform classifications of their respective subalgebras. A systematic use of the subalgebra structures allow us to construct several classes of invariant solutions, including travelling waves, centered waves and solutions involving monomials, exponentials and radicals.Comment: 30 page

Physics in Riemann's mathematical papers

Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore, Riemann's philosophical ideas are often in the background of his work on science. The aim of this chapter is to give an overview of Riemann's mathematical results based on physical reasoning or motivated by physics. We also elaborate on the relation with philosophy. While we discuss some of Riemann's philosophical points of view, we review some ideas on the same subjects emitted by Riemann's predecessors, and in particular Greek philosophers, mainly the pre-socratics and Aristotle. The final version of this paper will appear in the book: From Riemann to differential geometry and relativity (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Hydrodynamic Waves in Regions with Smooth Loss of Convexity of Isentropes. General Phenomenological Theory

General phenomenological theory of hydrodynamic waves in regions with smooth loss of convexity of isentropes is developed based on the fact that for most media these regions in p-V plane are anomalously small. Accordingly the waves are usually weak and can be described in the manner analogous to that for weak shock waves of compression. The corresponding generalized Burgers equation is derived and analyzed. The exact solution of the equation for steady shock waves of rarefaction is obtained and discusses.Comment: RevTeX, 4 two-column pages, no figure

A central limit theorem for the zeroes of the zeta function

On the assumption of the Riemann hypothesis, we generalize a central limit theorem of Fujii regarding the number of zeroes of Riemann's zeta function that lie in a mesoscopic interval. The result mirrors results of Soshnikov and others in random matrix theory. In an appendix we put forward some general theorems regarding our knowledge of the zeta zeroes in the mesoscopic regime.Comment: 22 pages. Incorporates referees suggestions. Contains minor corrections to published versio

Interface relaxation in electrophoretic deposition of polymer chains: Effects of segmental dynamics, molecular weight, and field

Using different segmental dynamics and relaxation, characteristics of the interface growth is examined in an electrophoretic deposition of polymer chains on a three (2+1) dimensional discrete lattice with a Monte Carlo simulation. Incorporation of faster modes such as crankshaft and reptation movements along with the relatively slow kink-jump dynamics seems crucial in relaxing the interface width. As the continuously released polymer chains are driven (via segmental movements) and deposited, the interface width $W$ grows with the number of time steps $t$, $W \propto t^{\beta},$ ($\beta \sim 0.4$--$0.8)$, which is followed by its saturation to a steady-state value $W_s$. Stopping the release of additional chains after saturation while continuing the segmental movements relaxes the saturated width to an equilibrium value ($W_s \to W_r$). Scaling of the relaxed interface width $W_r$ with the driving field $E$, $W_r \propto E^{-1/2}$ remains similar to that of the steady-state $W_s$ width. In contrast to monotonic increase of the steady-state width $W_s$, the relaxed interface width $W_r$ is found to decay (possibly as a stretched exponential) with the molecular weight.Comment: 5 pages, 7 figure